“It’s a huge burden on the American psyche to have a president go abroad when a sword of Damocles is hanging over them at home,” said Douglas Brinkley, a professor of history at Rice University and an expert on the presidency. “It turns our president, instead of representing the best of America on the road, into a traveling can of worms.”
Mr. Brinkley likened the timing of Mr. Trump’s trip to a visit Mr. Nixon made to the Middle East in 1974 as the Watergate scandal was closing in on him, and Mr. Clinton’s trip to Russia, Britain and Northern Ireland in 1998 during the height of the Monica Lewinsky scandal.
For his part, Mr. Trump, a confirmed homebody, has expressed dread about the trip, asking aides whether it can be shortened to five days from nine. His advisers concede that the intense schedule — dozens of interactions with leaders from the Middle East and Europe, over a range of delicate issues — could produce unscripted, diplomatically perilous moments.
Even beyond the tempests surrounding the president, Israeli officials expressed alarm about the unwillingness of Mr. Trump’s national security adviser, Lt. Gen. H. R. McMaster, to publicly affirm that the Western Wall, one of the holiest prayer sites in the Jewish faith, was part of Israel.
General McMaster’s statement came during a White House briefing about the trip that was largely overtaken by the furor over the intelligence disclosure. After going through the details of Mr. Trump’s travel — coffee with King Salman of Saudi Arabia, a wreath-laying in Israel — General McMaster was bombarded with questions like whether allies could trust the United States enough to share sensitive intelligence with it.
“I’m not concerned at all,” he said, asserting that Mr. Trump’s disclosures to Mr. Lavrov and the Russian ambassador, Sergey I. Kisylak, were “wholly appropriate.”
But General McMaster dodged when asked whether Mr. Trump believed the Western Wall was in Israel. The question arose after a report on Israeli television that an American official involved in planning the visit had rebuffed a request by Prime Minister Benjamin Netanyahu to join Mr. Trump on a visit to the wall because, the official said, it was not in Israel.
The White House disavowed that statement on Monday, saying it did not reflect the president’s thinking. But General McMaster confirmed that no Israeli leaders would join Mr. Trump in his visit to the wall — in line with longstanding American practice — and he declined to say whether Mr. Trump viewed the Western Wall as being part of Israel.
“That sounds like a policy decision,” he said.
Current American policy is to treat East Jerusalem, where the wall is, as Israeli-occupied territory. Israeli troops seized the area around the wall in 1967 during the Six-Day War, and it has become a highly visible symbol of the disputed nature of Jerusalem, which Palestinians also claim as their capital.
Mr. Trump’s new ambassador to Israel, David M. Friedman, visited the wall as one of his first acts after arriving in the country. And Mr. Trump promised repeatedly during the 2016 campaign that he would move the American Embassy to Jerusalem from Tel Aviv.
“He’s in real danger of blowing up Jerusalem as an issue that divides rather than unites two of the Abrahamic religions,” said Martin S. Indyk, an American ambassador to Israel under Mr. Clinton. “That part of the visit needs to be handled with extreme care.”
Mr. Trump’s disclosure of Israeli intelligence raises a separate set of issues. Mr. Netanyahu, who is determined to have a successful visit, is not likely to make an issue of this with the president, analysts said. But he will face intense pressure from his own intelligence services.
“For them, it is a question of how they acquire information and how they perceive threats against Israel,” said Dennis B. Ross, who has advised several presidents on Middle East issues. “This will inevitably produce a discussion about the ground rules.”
Aaron David Miller, another longtime Middle East diplomat, said, “This will likely break crockery, jeopardizing sources and additional information on ISIS operations.” But he added that Mr. Netanyahu “will see no reason to exacerbate the incident, and may well see some political advantage in giving Trump some cover and the benefit of the doubt.”
In Israel, some analysts speculated that Mr. Trump’s disclosure of Israeli intelligence might force his hand on the embassy, since he would need to make a good-will gesture to the Israelis.
“It would show that the president of the United States and his administration understand where lies the truth,” Avi Dichter, a former head of the Shin Bet and current Likud member of Parliament, said in an interview. “And that is what Jerusalem is for the state of Israel. It’s not just a symbolic step. It’s more profound than that.”
In Israel, government officials refused to comment on the report that Mr. Trump’s disclosure of intelligence was supplied by Israel. Some former officials familiar with Israel’s strategic and security relations with the United States said they did not have enough detailed information about the incident to assess what damage was done — or the possible fallout.
“The entire thing hinges on the specifics,” said Eran Lerman, a former deputy director of Israel’s National Security Council, who handled Israel’s strategic dialogue with the United States. “Yes, you try to protect your sources as best you can. But on the other hand, if you have actionable intelligence, you want to talk to people who can take action.”
Mr. Lerman, who teaches at Shalem College in Jerusalem and is a senior researcher at the Begin-Sadat Center for Strategic Studies at Bar Ilan University, pointed to what he called Mr. Trump’s “lack of serious grounding in intelligence craft.” But he added, “I cannot judge if the president made the right call or the wrong call.”
Israel and the United States have no choice but to share intelligence, he said, though some rewriting of the ground rules might now be necessary. “At the end of the day, the community of like-minded nations cannot afford to tear the fabric of cooperation apart,” he said, “but there may be a need to sew it with more sturdy threads here and there.”